In the above equation, \(g\)  is the redshift factor, while \(\nu _{\rm obs}\)  and \(\nu _{\rm em}\)  denote the observed photon frequency and radiated photon frequency, respectively. In the quintessence Hayward black hole space-time (REF ), the redshift factor is \(g = f(r)^{1/2}\) . Assuming that the emission is monochromatic with rest frame frequency \(\nu _{\rm t}\)  and the emission radial profile is \(1/r^2\)  [1]}, the specific emissivity takes the form
\(j (\nu _{\rm em}) \propto \frac{\delta (\nu _{\rm em}-\nu _{t})}{r^2}.\) 
